Numerical relativity with characteristic evolution, using six angular patches

Abstract

The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50.

12 pages, 5 figures, submitted to CQG (special NFNR issue)

References in corpus (3)

• A numerical study of the quasinormal mode excitation of Kerr black holes
• Black Hole Excision with Multiple Grid Patches
• On characteristic initial data for a star orbiting a black hole

Cited by in corpus (5)

• Calibration of Moving Puncture Simulations
• Strategies for the Characteristic Extraction of Gravitational Waveforms
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• A framework for large-scale relativistic simulations in the characteristic approach
• Quasi-Normal Modes of a Schwarzschild White Hole